In each step, define a new ftc by using the hypernetted chain relation:

(H.32)

Note that e1(r) in this case is the Lennard-Jones potential.

In each step, define a new fdc by Fourier transforming ftc and fdc, applying the Fourier-transformed
Ornstein-Zernike equation to get a new , and inverse Fourier-transforming to get a new fdc. We
do this because the Fourier-transformed Ornstein-Zernike equation is much easier to deal with (the
spatial integral becomes a product when Fourier-transformed):

(H.33)

Here k is the frequency variable and is the Fourier transform of f. This can be rearranged to
give

(H.34)

So we Fourier-transform ftc and fdc to get and , apply Equation H.34, and then transform
back.

The two previous steps are repeated until the solutions for ftc and fdc are no longer changing.
Some attention to numerical stability is needed, especially if ρ* is high and T* is low.

Plot your results for nine cases as follows: three values of ρ* (0.1, 0.4, 0.8) and three values of T* (0.5, 1.0,
1.5).

Given the results from Exercise H.1, calculate the potential of mean force that atoms see in this case.
Plot the emf for the nine cases from Exercise H.1.

Calculate the magnitude of the dipole moment (in Debye) for a water molecule given the geometry of
the SPC model.

Consider hard spheres of radius a.

What is the closest approach of the centers of two spheres?

What is the doublet potential for the interaction between the two spheres?

Calculate the excluded volume. How does the excluded volume compare with the volume of one
of the spheres?

Show that the nonintegrability of the Coulomb pair potential guarantees that physical systems must be overall
electroneutral.

Using the equation for monopole interaction potentials, explain why sodium chloride might be expected to be
a crystalline solid when dry but dissolves when exposed to water.